-
Name: ______________________________________ Class:
______________ Date: ____________
Unit 5: Butterflies, Pinwheels, & Wallpaper
Directions: Please complete the necessary problems to earn a
maximum of 10 points according to the
chart below. Show all of your work clearly and neatly for
credit- which will be earned based on
completion rather than correctness.
I can complete transformations of shapes on a coordinate
plane.
Lesson Practice problems Options Maximum
Points
Lesson 1: Flipping on a Grid
1, 2, 3, 8
3 Points
Lesson 2: Sliding on a Grid
4, 5, 9 2 Points
Lesson 3: Spinning on a Grid
6, 7, 10 2 Points
Lesson 5: Parallel Lines, Transversals, and Angle Sums
11, 12, 13, 14 3 Points
______/ 10 Points
-
Name: ______________________________________ Class:
______________ Date: ____________
For Exercises 1 – 7, use the figure below and find the image of
the figure after each transformation.
1. Complete the table showing the coordinates of points A – E
and their images after a reflection in the y – axis.
Point A B C D E Original Coordinates (-5, 1) (-2, 5) (0, 2) (-2,
3) (-3, 0)
Coordinates After a y-axis Reflection (5, 1) (2, 5) Coordinates
After a x-axis Reflection (-5, -1) (-2, -5) (-2, -3)
Coordinates After a x-axis Reflection Followed By a y-axis
Reflection
(2, -5) (0, -2) (2, -3)
a. Draw the Image.
b. Write a rule relating coordinates of key points and their
images after a reflection in the
y-axis: (x, y) ( ____ , ____ ).
2. Add a row to your table for Exercise 1 to show the
coordinates of points A – E and their images after a reflection in
the x- axis.
a. Draw the image. b. Write a rule relating coordinates of key
points and their images after a reflection in the
x-axis: (x, y) ( ____ , ____ ).
3. Add another row to your table from Exercise 1 to show the
coordinates of points A – E and their images after a reflection in
the x-axis, followed by a reflection in the y-axis.
a. Draw the image. b. Write a rule relating coordinates of key
points and their images after bother reflections:
(x, y) ( ____ , ____ ). c. Multiple Choice. What single
transformation in this Investigation has the same effect as
the sequence of two line reflections? i. half- turn
rotations
ii. 1 unit to right, down 5 units translation iii.
-
Name: ______________________________________ Class:
______________ Date: ____________
4. Complete the table showing the coordinates of points A – E
and their images after a translation
that “moves” point B to point (3, 4).
Point A B C D E Original Coordinates (-5, 1) (-2, 5) (0, 2) (-2,
3) (-3, 0)
Coordinates After Translating B to (3, 4) (0, 0) (5,1) (2, -1)
Coordinates After Translating B’’ to (-1, 0) (-4, -4) (-1, 0) (1,
-3)
a. Draw the image. b. Write a rule relating coordinates of key
points and their images after the translation: (x,
y) ( ____ , ____ ).
5. Add a row to your table from Exercise 4 to show the
coordinates of points A – E and their images after the first
translation, followed by a translation that “moves” points B’ to
(-1, 0).
a. Draw the image. b. Write a rule relating coordinates of key
points and their images after the second
translation: (x, y) ( ____ , ____ ). c. Write a rule relating
coordinates of key points and their images after the sequence
of
the two translations: (x, y) ( ____ , ____ ). d. Multiple
Choice. What single information is equivalent to the sequence of
the two
translations? i. half- turn rotations
ii. 1 unit to right, down 5 units translation iii.
-
Name: ______________________________________ Class:
______________ Date: ____________
6. Complete the table showing the coordinates of points A – E
and their images after a counterclockwise rotation of 90° about the
origin.
Point A B C D E Original Coordinates (-5, 1) (-2, 5) (0,2) (-2,
3) (-3, 0)
Coordinates After a 90° Rotation (-1, -5) (-2, 0) (-3, -2)
Coordinates After a 180° Rotation (5, -1) (0, -2) (3, 0)
a. Draw the image. b. Write a rule relating coordinates of key
points and their images after a rotation of 90°:
( x, y) ( ____ , ____ ).
7. Add a row to your table from Exercise 6 to show the
coordinates of points A – E and their images after two
counterclockwise rotations of 90° about the origin.
a. Draw the image. b. Write a rule relating coordinates of key
points and their images after both rotations:
(x, y) ( ____ , ____ ). c. Multiple Choice. What single
transformation is equivalent to the sequence of the two
rotations? i. half- turn rotations
ii. 1 unit to right, down 5 units translation
8.
-
Name: ______________________________________ Class:
______________ Date: ____________
Complete the table showing the coordinates of points A – C and
their images after a reflection in the line
y = x.
Point A B C Original Coordinates (0, 2) (1, 5) (3, 5)
Coordinates After a Reflection in y = x (5, 1) Coordinates After
a Reflection of Triangle A’B’C’ (2, 0) (5, -3)
b. Draw the image and label the vertices A’, B’, and C’.
c. Add a row to your table to show the coordinates of points A –
C and their images after a
reflection of triangle A’B’C’ in the axis.
d. Draw the image and label the vertices A”, B”, and C”.
e. Draw the image of triangle ABC after the same two reflection,
but in the reverse order.
That is, reflect triangle ABC in the x-axis and then reflect its
image, triangle A’B’C’ in the
line y = x. What does the result suggest about the commutativity
of a sequence of line
reflections?
9.
i. Translate ABC according to the rule (x, y) (x + 2, y – 3).
Label its image A’B’C’.
ii. Translate ABC according to the rule (x, y) (x – 4, y – 6).
Label its image A”B”C”.
-
Name: ______________________________________ Class:
______________ Date: ____________
b. Use the coordinates of the vertices of triangle ABC and its
two images to compare the
slopes of each pair of line segments.
The slopes of AB and A’B’ are both ____.
The slopes of AC and A’C’ are both ____.
The slopes of CB and C’B’ are both _____.
The slopes of AB and A”B” are both ____.
The slopes of AC and A”C” are both ____.
The slopes of CB and C”B” are both _____.
c. Multiple Choice. What do your results from parts (a) and (b)
say about the effect of
translations on the slopes of lines? About the relationship
between a line and its image
under a translation?
i. Translations ignore the slope of lines and does not map lines
onto parallel lines.
ii. Translations preserve slopes of lines and maps lines onto
parallel lines.
10. a. Use triangle ABC from Exercise 8. Draw triangle ABC on a
coordinate grid and its image
after a 180° rotation about the origin. Label the Image
A’B’C’.
b. Use the coordinates of the vertices of triangle ABC and its
image to compare the slopes
of each pair of line segments.
Slopes of both AB and A’B’ are both _____.
Slopes of both AC and A’C’ are both _____.
-
Name: ______________________________________ Class:
______________ Date: ____________
Slopes of both CB and C’B’ are both ______ .
c. What do your results from part (a) and (b) say about the
effect of half-turns or 180°
rotations on the slopes of line? About the relationship between
a line and its image
under a 180°
11. In the diagram below, line L1 and L2 are parallel. What are
the measures of angles a – g?
*** remember opposite angles equal the same measurement,
adjacent angles add up to 180°.
Angles a, c, and e all measure ______.
Angles b, d, f, and g all measure _____.
12. What are the measures of angles a and b in the triangle?
*** remember adjacent angles add up to 180°.
13. What is the value of x in the diagram?
** remember angles in a Triangle add up to 180°.
-
Name: ______________________________________ Class:
______________ Date: ____________
14. The diagram shows parallelogram ABCD with one diagonal DB.
Assuming only that opposite
sides of any parallelogram are parallel:
a. Which angles are congruent? How do you know?
b. How can you be sure that triangle ABD is congruent to
triangle ADB? What are the
corresponding vertices, sides, and angles?
c. How does the congruence of triangles ABD and ADB guarantee
that, in a parallelogram,
opposite sides are the same length?
Exit Ticket Level of Understanding
After finishing this investigation you should be comfortable
doing the following: -using coordinate methods to study flips,
turns, and slides. -understanding the properties of parallel lines.
-understanding the properties of angles in triangles